Like many families, mine has been divided by politics in recent years. I am British; my dad has returned to his native Hungary. I work for the Guardian; he has become a supporter of Hungary’s nationalist prime minister, Viktor Orbán. It had become a festering sore. He loves talking politics, and resented the fact that he couldn’t discuss politics with me. I couldn’t talk about it, because I resented his politics.

So we decided to go on a road trip together. We’d spend seven days in a car, travelling across Hungary and its political spectrum to have it all out. What could possibly go wrong?

Hungary has been in the news a lot recently (nobody cared about it for years). Orbán has set about building what he calls an “illiberal democracy” and leading a nationalist surge in May’s European parliamentary elections. This winter there have been opposition protests on the streets. The battle lines are clear to many commentators: on the one side are the nationalists/populist right/far right; on the other, the liberals/federalists/globalists – choose your terms according to which side you’re on.

It was this political faultline we set off to explore as the Hungarian winter set in last year. We planned our journey to take us through symbolic parts of Hungary’s history and present: a commemoration of the Hungarian revolution of 1956 (against the communist dictatorship), a formative event for both my father, who remembers being locked in a cellar as a frightened six-year-old, and modern Hungary; Miskolc, a post-industrial city that exemplifies the lack of economic progress since the fall of communism in 1989; and back to the rural roots of our family, and the bedrock of Orbán’s support.

It was not difficult to find evidence of the fear about national identity that many on the left now find so alarming. It was there in the mayor I met, from Orbán’s Fidesz party, determined to “dream big” from his small southern village. It was there in the young man who had worked in supermarkets and kitchens in England, but returned home to answer an “inner calling”. It was even clearer when we travelled deep into Romania, and met ethnic Hungarians keeping alive their traditions – threatened first by the redrawing of national borders that was a feature of 20th-century central Europe and now, they felt, by globalisation. But I also saw it among passionate housing activists protesting against Orbán. And in two young female artists who had moved back to Miskolc in the hope of sparking cultural regeneration.

By no means were all these people either devoted fans of Orbán or his version of nationalism, or opposed to him. Hungary can feel like a very divided place, yet so many of the people we met along the way had more in common than they might imagine. I see that now with my father too, and feel closer to him than I realised – even if we still disagree over much.

I learned that he too feels he is voting in hope, rather than the hatred and resentment often ascribed to people like him. I learned how much history matters in shaping those hopes – and fears. Identity matters too: people’s attachment to place, the need to pass that identity down and preserve it from perceived threats.

It’s hard to admit that you are wrong in a family argument. It brought home to me how the binary way we increasingly talk about politics is destructive and counterproductive. I often felt put in a box by my father as an “orthodox liberal with no sense of patriotism”. I didn’t realise how much I had done the same to him. I think we now both understand that it is not so simple. Anyone who wants to counter the appeal of politicians like Orbán needs to learn the same lessons. And they cannot leave issues of identity, place and nation for those on the right to own.

Too many people seem to find this hard to accept. Take the joint letter from 30 liberal intellectuals published in several papers, including the Guardian, on Saturday. The writers, including Salman Rushdie, Bernard-Henri Lévy and Simon Schama, wrote of “a new battle for civilisation” and vowed to lead a “new surge” to stop Europe perishing “beneath the populist waves”. With my Hungary trip fresh in my mind, I feel this approach is part of the problem. I share their concerns, but their letter is a gift to the likes of Orbán – trying to combat his arguments by confirming that he is right.

They write of a “noxious climate” (which the tone of the letter duly does its bit to perpetuate) and a “politics of disdain for intelligence and culture” – but show nothing but contempt for the people who vote for this. People like my dad. The only mention of national identity is to call it an “abstraction” that exists “only in the imagination of demagogues”.

We ended our journey by going to see Orbán address his supporters. He spoke powerfully of Hungary’s centuries-long struggles for freedom from oppression and occupations. And of a battle for Europe between two opposing worldviews. He positioned himself and his followers as the defenders of both national and European values, of culture and freedom. Sound familiar? He went on to talk about migrants and elites removed from their national roots in terms that I felt almost personally attacked by. If your goal is to divide people, make some of them feel under attack or misrepresented, by all means take a leaf out of Orbán’s book. Otherwise, better to start by listening, and reflecting on what your side can do better to connect with those who don’t already agree with you.

• John Domokos is a Guardian film-maker. Watch his film, Orbán, my dad and me, here